Dear pick(3-4) hunters!!!
I found this article and I think it's very interesting!!!
I know you are asking, "what the heck is a vampire number!?" I don't blame you, that's exactly what I thought when I bumped into them. Well, here's the story.... It all began when I happened to read the "Brain Bogglers" page in the June '95 issue of Discover magazine. I noticed that the author was Clifford Pickover, whom I knew from some of the fractal programs that I have of his, and from some of the wonderful books he has written. I usually don't bother with the Brain Boggler page, because I never have the patience to try and figure them out. But this one was different. Rather than try and explain it, here it is...
Brain Bogglers Interview With A Number by Clifford Pickover
If we are to believe best-selling novelist Anne Rice, vampires resemble humans in many respects but live secret lives hidden among mortals. There are also vampires in the world of mathematics, numbers that look like normal figures but bear a disguised difference. They are actually the products of two progenitor numbers that when multiplied survive, scrambled together, in the vampire number. Consider one such case: 27 x 81 = 2,187. Another vampire number is 1,435, which is the product of 35 and 41. I define true vampires, such as the two previous examples, as meeting three rules. They have an even number of digits. Each one of the progenitor numbers has half the number of digits of the vampire. And finally, a true vampire number is not created simply by adding zeros to the ends of numbers, as in:
270,000 x 810,000 = 218,700,000,000.
True vampires would never be so obvious. Vampire numbers secretly inhabit our number system, but most have been undetected so far. When I grabbed my silver mirror and wooden stake and began my search for them, I found, in addition to the two listed above, five other four-digit vampire numbers. Can you find the others? Can you find any vampire numbers with more digits in them?
All of the 4 digit TRUE vampires.
A number v = xy with an even number (n) of digits formed by multiplying a pair of n/2-digit numbers (where the digits are taken from the original number in any order) x and y together is known as vampire number. Pairs of trailing zeros (Both the numbers have a trailing zero) are not allowed. If v is a vampire number then x and y are called its "fangs." Examples of 4-digit vampire numbers include
1. 21 x 60 = 1260
2. 15 x 93 = 1395
3. 35 x 41 = 1435
4. 30 x 51 = 1530
5. 21 x 87 = 1827
6. 27 x 81 = 2187
7. 80 x 86 = 6880
Vampire number countsDigits | Vampire ratio | Vampires with at least f different fang pairs | Vampire equations | Prime vampires |
f=1(all vampires) | f=2 | f=3 | f=4 | f=5 |
4 | 1/1286 | 7 | 0 | 0 | 0 | 0 | 7 | 0 |
6 | 1/6081 | 148 | 1 | 0 | 0 | 0 | 149 | 5 |
8 | 1/27881 | 3228 | 14 | 1 | 0 | 0 | 3243 | 57 |
10 | 1/82984 | 108454 | 172 | 0 | 0 | 0 | 108626 | 970 |
12 | 1/204980 | 4390670 | 2998 | 13 | 0 | 0 | 4393681 | 26653 |
14 | 1/431813 | 208423682 | 72630 | 140 | 3 | 1 | 208496456 | 923920 |
Vampire ratio is (n-digit vampire numbers)/(n-digit integers) and not a ratio of performed tests.
Vampire equations are all equations of the form vampire = fang1 · fang2, i.e. each vampire number counts for each different fang pair. Prime vampires obviously only have one fang pair.
The vampire equations for all table counts below 15 are on this page.
First 15 vampires with exactly 2 fang pairs125460 = 204 · 615 = 246 · 510 | 11930170 = 1301 · 9170 = 1310 · 9107 |
12054060 = 2004 · 6015 = 2406 · 5010 | 12417993 = 1317 · 9429 = 1347 · 9219 |
12600324 = 2031 · 6204 = 3102 · 4062 | 12827650 = 1826 · 7025 = 2075 · 6182 |
13002462 = 2031 · 6402 = 3201 · 4062 | 22569480 = 2649 · 8520 = 4260 · 5298 |
23287176 = 2673 · 8712 = 3267 · 7128 | 26198073 = 2673 · 9801 = 3267 · 8019 |
26373600 = 3600 · 7326 = 3663 · 7200 | 26839800 = 2886 · 9300 = 3900 · 6882 |
46847920 = 4760 · 9842 = 6290 · 7448 | 61360780 = 7130 · 8606 = 7613 · 8060 |
1001795850 = 10170 · 98505 = 19701 · 50850 |
"Then give to the world the best you have, And the best will come back to you."
Madeline Bridges